Understanding the Function f(x) = |x| – 2: Exploring the Absolute Value Function and its Graph

f(x) = |x| – 2

To understand the function f(x) = |x| – 2, let’s break it down into parts

To understand the function f(x) = |x| – 2, let’s break it down into parts.

The |x| represents the absolute value of x. The absolute value function produces the distance between x and 0 on a number line, regardless of whether x is positive or negative.

Let’s consider two scenarios:

1. If x is positive or zero, |x| = x. Therefore, f(x) = x – 2.

2. If x is negative, |x| = -x. Therefore, f(x) = -x – 2.

Let’s further analyze the function in these scenarios:

1. If x is positive or zero:
For any positive or zero value of x, the function f(x) = x – 2. For example, if x = 3, then f(x) = 3 – 2 = 1. This means that the output of the function is two less than the input value in this case.

2. If x is negative:
For any negative value of x, the function f(x) = -x – 2. For example, if x = -3, then f(x) = -(-3) – 2 = 1. Again, the output of the function is two less than the input value, but with the negative sign.

So, the value of f(x) depends on whether x is positive or negative.

To plot the graph of f(x), you can create a table of values for x and calculate the corresponding values of f(x). For instance:

x | f(x)
———–
-3 | 1
-2 | 0
-1 | -1
0 | -2
1 | -1
2 | 0
3 | 1

By plotting these points on a coordinate plane, you will notice that the graph of f(x) is V-shaped, with the vertex located at (0, -2). The graph extends infinitely in both the positive and negative x-directions.

I hope this explanation helps you understand the function f(x) = |x| – 2. Let me know if you have any further questions!

More Answers: